CAT (QA) PYQs

If the sum of squares of two numbers is $97$, then which one of the following cannot be their product?

If $a$ and $b$ are integers such that $2x^2 - ax + 2 > 0$ and $x^2 −bx + 8 \geq 0$ for all real numbers $x,$ then the largest possible value of $2a-6b$ is

The number of integers n that satisfy the inequalities $|n -60| < |n-100| <| n-20|$ is